(extended rewrite of http://lesswrong.com/lw/lpf/the_truth_about_mathematical_ability/)

There's widespread confusion about the nature of ability, for a variety of reasons:

    Most people don't know what it is.
    Most people don't know enough statistics to analyze the question properly.
    Most people are not very metacognitive.
    Very few people have more than a casual interest in the subject.

If ability's nature were exclusively an object of intellectual interest, this would be relatively inconsequential. For example, many people are confused about Einstein’s theory of relativity, but this doesn’t have much of an impact on their lives. But in practice, people’s misconceptions about ability seriously interfere with their own ability to learn, something that hurts them both professionally and emotionally.

I have a long standing interest in the subject. Unfortunately I do not have any expertise, being too young to have acquired such credentials.

I’ve thought about writing about ability for a long time, but there was a missing element: I myself had never done genuinely original and high quality work. Indeed, I still have not; using R would be cheating, since to qualify for my notion of genuinely original, I would have to have started from the bare earth, smelted the ore, refined them into a computer, and written an entire operating system. This continued failure of originality has sharpened my understanding of the issues.

This is a post where I try to clarify the situation. I don't think it has a point, other than sarcasm and making fun of certain people.

What is up with Jobs?

I was saddened to learn of the death of Steve Jobs several years ago. He's the person who I identify with the most on a personal level, and I had hoped to have the chance to meet him. I hesitated as I kept the last sentence, because I'm not certain it will cause every reader to roll their eyes. The material below should make my state of mind clear:

    “Steve Jobs's deep experience in hardware mass production (early Apple, NeXT) has been brought to bear in creating an unrivaled exclusive supply chain of advanced technology literally years ahead of anyone else on the planet,” Anonymous wrote. “Apple products are superior, since Jobs was such a visionary and perfectionist. What consumer wouldn’t feel great about purchasing a device developed by such a person." — Michael Pennington, Samsung’s vice president of sales operations and head of national sales for Samsung Telecommunications America,

    "When I was at Stanford as a student, I went to Jobs's commencement speech... I enjoyed the atmosphere around him very much ... If we look at the decisions and patterns displayed by those who we believe to have an obsessive pursuit, we can see a theme of sacrifice and suffering as a result of prioritizing that passion over everything else." — Stanford students

    "[Tom] knew how it felt to have no privacy whatsoever when he was working right here, in a little Californian town called Cupertino, in a legendary place located in One Infinite Loop. [...] The Worldwide Loyalty Team reported directly to Steve Jobs." -- Gawker. "Steve Jobs was a great person. he was ….. a god." — Sandy

    "Suffice to say, I was one heck of a Mac bigot in those days. I idolized Steve Jobs, traveled faithfully and constantly to the Cupertino Mecca Apple called home, had ongoing dialogues with the now-infamous Apple CEO John Sculley and was invited to Steve Wozniak's palatial home for a holiday party." — Robert C. DeMarzo

Based on these remarks alone, it should be very hard to imagine how anyone could want to be more like Jobs. But when I read http://time.com/3698686/gifted-and-talented/, it's hauntingly familiar. Although more than three decades of research from Stanford psychologist Carol Dweck and others have support the belief in developing one's potential, and in particular shown that individual struggle is critical to higher learning, there is a persistent belief that this is not "what counts". There are people who cheat, who look for the easy way out.

Jobs writes:

    “Everything around you that you call life was made up by people that were no smarter than you, and you can change it, you can influence it, you can build your own things that other people can use... Your time is limited, so don’t waste it living someone else’s life. Don’t be trapped by dogma – which is living with the results of other people’s thinking. Don’t let the noise of other’s opinions drown out your own inner voice. And most important, have the courage to follow your heart and intuition. They somehow already know what you truly want to become. Everything else is secondary”

When I checked http://www.lewisandlewis.com.au/assessments-tests/giftedness/was-steve-jobs-gifted-2/, they scoffed and said that of course Jobs was gifted and smarter than those around him – he was engaging in a sort of bragging, along the lines of "I'm so awesome that even though I'm not smart I am still one of the greatest people ever."  It is hard to reconcile Jobs's self-description with his above-average performance. But I was stunned by the article's willingness to ignore the remarks of somebody so great out of hand. In fairness, Steve Jobs was probably following the work of Carol Dweck with great interest, and simply stated what would help the students, rather than the truth.

What is up with me?

I went to a different school every two years. The high school I went to did not even offer a course AP Calculus BC; I took their AB class, spent a few days studying the last two chapters of the textbook, and got a 5 on the AP exam. From this, people understandably inferred that I'm unusually brilliant. Having received a number of awards to that effect, I tend to agree. When I point out that things are not always this way, and that I have in fact received several B's and even one C throughout my academic career, along with numerous disciplinary incidents, their reactions tended to be along the lines of "so what?". It's not at all mysterious to me why I got those B's and C's. In fact, if you were to ask my teachers, it would be obvious; I simply wasn't paying enough attention to their course. The disciplinary incidents are harder to explain away; currently, a power coup by the vice-principal seems to be the most self-serving explanation.

Aside from taking AP Calculus BC during my freshman year, I also took the SAT in 6th grade. I only scored around 650, but there were still ~20 students who scored higher than me in the state of Colorado and were invited to the awards ceremony. The only problem was that they were all older than me. But just looking at my SAT score, people would think very unlikely that I could have gotten a 5 on the AP Calculus BC in my freshman year.

As far removed my ability is from Jobs's, we have at least one thing in common: our respective performances on some commonly used measures of ability are about what most people would expect based on our accomplishments.

Hopefully these examples suffice to make clear that whatever ability is, it's not precisely "what the SAT measures." What the SAT measures is highly relevant, but still not the most relevant thing.

What does the SAT measure?

Just for fun, let's first look at what the College Board has to say on the subject. According to The Official SAT Study Guide

    The SAT does not test logic abilities or IQ. It tests your skills in reading, writing and mathematics – the same subjects you're learning in school. [...] If you take rigorous challenging courses in high school, you'll be ready for the test.

Some of you may be shocked by the College Board's disingenuousness without any further comment. How would they respond to my own situation? Well, they would point out that I was still in middle school, and so was unlikely to score well. Indeed, I took it again as a high school junior and received an 800 on the mathematical section. But then I took it a third time as a senior, and received only a 780 on the math section; I instead got an 800 on the verbal. Why the variance? Their strongest response would be to say that there is always some random noise on the test. I prefer to say that it discriminates based on people's interests.

I don’t think that rigorous, academic challenging courses build skills that enable high school students to solve these questions. It is more the other way around; the students build up skills to solve the questions posed in rigorous, academic challenging courses, which transfer occasionally to other disciplines such as the SAT. As my own experience shows, many questions can be solved by a very smart 6th grader who hasn’t studied algebra or geometry. (I took those in 7th and 8th grades, respectively). However, to do exceptionally requires advance preparation and/or taking the test more than once.

The SAT Subject Tests are much more closely connected with what students (are supposed to) learn in school. As such, I did not bother studying for it at all, and received an 800 anyways.

At least for me, the SAT did give me, a smart student from a relatively underprivileged background, the chance to attend a "high quality"  private college (top 10 in mathematics, No.4 in the 2012 US news rankings), on a nice scholarship – it turns out that (sticker) price does not imply quality. Although the university did indeed have a rigorous curriculum, the occasional incidents such as exploding toilets, plastic in the dining hall's food, and binge drinking, led me to believe that the university has become a harmful force in society. http://nymag.com/daily/intelligencer/2014/09/take-away-harvards-nonprofit-status.html characterizes Harvard as a giant hedge fund masquerading as a non-profit college; I'm not certain where universities keep all their money, but it certainly isn't spent on student living conditions.

Singly exceptional gifted children

Let’s return to the question of reconciling my very strong AP Calculus BC performance with my relatively low SAT score in 6th grade. I could have taken up the notion that I had always had very high intelligence and that that’s why I was able to learn well by saying “No, you’re wrong, my SAT score shows that I don’t have very high intelligence, the reason that I was able to learn well is that I really love the subject.” But that would oversimplify things. In particular, it leaves the problem of time; the SAT was 6th grade, while the Calculus BC was freshman year. Perhaps the largest part of why I failed in 6th grade was that I was too young at the time, too inexperienced. But what made me different in freshman year? The simple answer is they were measuring different things; I was around the 90th percentile in the SAT, while at least 40% of people who take it get a 5 on the AP Calculus BC every year, at least since 1999. How unique am I, compared to Steve Jobs?

Partial answers to these questions come from the literature on so-called “Twice Exceptional” (2e) children. The label is used broadly, to refer to children who are intellectually gifted and also have some sort of disability. For example, the original author of this post had exceptionally high reasoning abilities, but only average short term memory and processing speed. I do not appear to have such problems; I was tested, and all systems functioned above average. I am a "singly exceptional gifted child". Unfortunately, even this is a disability; I have an exceptional ability to focus, often to the concern of others around me. For example, I was (re)writing this essay instead of grading papers at $11 an hour. Since it impairs my ability to work, this qualifies as a mental disability. The psychiatrists tell me I have type I bipolar disorder, and should take drugs to make me less easily distracted, but I thought I should check with LW first before making a decision, since I'm not exactly certain who's suffering from the cognitive biases.

Jobs wrote:

    Remember, the sixties happened in the early seventies, and that's when I came of age; and to me, the spark of that was that there was something beyond what you see every day. It's the same thing that causes people to be poets instead of bankers. And I think that's a wonderful thing. I think that same spirit can be put in to products, and those products can be manufactured, and given to people, and they can sense that spirit.
   
Readers are welcome to speculate on what Jobs had in mind in writing this; I will just mentioned that the sixties are occasionally advertised as an age of "sex, drugs, and rock-n-roll", and that I happen to be flying to the International Students for Liberty Conference in D.C. this weekend. (Please PM me if you're there!)